sigex.acf: Compute the autocovariance function of a differenced latent...

View source: R/sigex.acf.r

sigex.acfR Documentation

Compute the autocovariance function of a differenced latent component

Description

Background: A sigex model consists of process x = sum y, for stochastic components y. Each component process y_t is either stationary or is reduced to stationarity by application of a differencing polynomial delta(B), i.e. w_t = delta(B) y_t is stationary. We have a model for each w_t process, and can compute its autocovariance function (acf), and denote its autocovariance generating function (acgf) via gamma_w (B). Sometimes we may over-difference, which means applying a differencing polynomial eta(B) that contains delta(B) as a factor: eta(B) = delta(B)*nu(B). Then eta(B) y_t = nu(B) w_t, and the corresponding acgf is nu(B) * nu(B^-1) * gamma_w (B).

Usage

sigex.acf(L.par, D.par, mdl, comp, mdlPar, delta, maxlag, freqdom = FALSE)

Arguments

L.par

Unit lower triangular matrix in GCD of the component's white noise covariance matrix.

D.par

Vector of logged entries of diagonal matrix in GCD of the component's white noise covariance matrix.

mdl

The specified sigex model, a list object

comp

Index of the latent component

mdlPar

This is the portion of param corresponding to mdl[[2]], cited as param[[3]]

delta

Differencing polynomial (corresponds to eta(B) in Background) written in format c(delta0,delta1,...,deltad)

maxlag

Number of autocovariances required

freqdom

A flag, indicating whether frequency domain acf routine should be used.

Details

Notes: this function computes the over-differenced acgf, it is presumed that the given eta(B) contains the needed delta(B) for that particular component. Conventions: ARMA and VAR models use minus convention for (V)AR polynomials, and additive convention for (V)MA polynomials. SARMA and SVARMA use minus convention for all polynomials.

Value

x.acf: matrix of dimension N x N*maxlag, consisting of autocovariance matrices stacked horizontally


jlivsey/sigex documentation built on May 25, 2024, 4:17 a.m.